Stability of a Generalization of Cauchy's and the Quadratic Functional Equations in Quasi-Banach Spaces

Thanatporn Bantaojai, Cholatis Suanoom

Abstract

In this paper, we extend and improve the concept of Almahalebi [M. Almahalebi, Stability of a generalization of Cauchy's and the quadratic functional equations, J. Fixed Point Theory Appl. 20 (12) (2018)] to qusic-Banach spaces by using the fixed point method. Second, we investigate the stability of the following generalization of Cauchy’s and the quadratic functional equations

$$ \sum_{k=0}^{n-1}f(x+b_k y)=nf(x)+nf(y),$$

where $n \in N_2 b_k =\exp(2i\pi k)$ for $ 0 \leq k \leq n-1,$ in quasi-Banach spaces. Moreover, we obtain the hyperstability results of this equation by using the fixed point method.